A

X Gk,j + P + VuQk,1 +X V2,iQk,i + Qfat j>1 i>1 J

where Qfat is the relevant fatigue load (e.g. traffic load or other cyclic load).

2.6.1 Combinations of actions for the ultimate limit states verification of a building

EN1990 Annex A1 gives rules for combinations of actions for buildings, on the basis of symbolic expressions and recommended values (or of values given in the National Annex) of partial factors to be applied to actions in the combinations. Eurocodes allow combinations of actions to contain two or more variable actions.

In general, for ultimate limit states, values of partial factors are subdivided in three sets (A, B and C), given in Tables [A1.2(A)-EN1990] to [A1.2(C)-EN1990], which are combined in the following table.

Table 2.15. Sets A, B and C of partial factors y for actions

Actions

Permanent actions Gk

Predominant variable action Qk,1 (Note 2)

Non predominant variable actions Qk,i (Note 2)

Unfavourable

Favourable

Set A

1,10

0,90

1,5

1,5 ■ Vo.t

Set B (Note 1)

(eq.6.10)-EN1990

1,35

1,00

1,5

1,5 ■ Vo,t

or alternatively the most unfavourable between the two following:

(eq.6.10a)-EN1990

1,35

1,00

1,5 ■ Vo,i

1,5 ■ Vo,t

(eq.6.10b)-EN1990

0,85 ■ 1,35

1,00

1,5

1,5 ■ Vo,t

Set C

1,00

1,00

1,30

1,30

Note 1: ea. 6.10 or alternatively the most unfavourable between ea. 6.10a and ea. 6.10b is used. The choice is made in the National Annex. In case of 6.10a and 6.10b, the National annex may in addition modify 6.10a to include permanent actions only.

Note 2: The partial factor of favourable variable actions should be taken as 0.

Depending on the limit state under consideration, values from one or more sets should be used, as indicated in the following table.

Table 2.16. Sets of partial factors to be used for ULS

Limit state

Set of partial factors to be used

EQU - Static equilibrium

Set A

STR - Design of structural members not involving geotechnical actions

Set B

STR - Design of structural members involving geotechnical actions (foundations, piles, basement walls, etc.)

GEO - Breaking or excessive deformation of ground

Approach 1(*): Apply in separate calculations design values from Set B and Set C to all actions. In common cases, the sizing of foundations is governed by Set C and the structural resistance is governed by

Approach 2: Apply Set B to all actions

Approach 3: Simultaneously apply, in the same calculation, Set B to actions on the structure and Set C to geotechnical actions

The choice of approach to be used for STR/GEO verification is given in the National Annex.

Combinations obtained with sets A, B and C of partial factors with EN 1990 recommended values are given below. Note that the partial factor of variable actions should be taken as 0 where these actions are favourable.

Combinations of actions with Set A of partial factors (EQU)

Si1'1, Gk,Sup + 0,9 • Gkj-mf) +1,5 • Qkl + £ 1,5 ■ ¥oiQki i>i i>1

In this combination the favourable part of a same action is multiplied by 0,9 and the unfavourable by 1,1. For example, in the verification of holding down devices for the uplift of bearings of a continuous beam, the self weight of spans that give a stabilising effect should be multiplied by 0,9 whereas the self weight of spans that give destabilising effect should be multiplied by 1,1 (see Example 2.1).

Combinations of actions with Set B of partial factors (STR/GEO) Either

E (1.335 • Gkj,Sup +1,0 • Gkj,inf) +1,5 • Qk.1 + £ 1,5 • Vo,IQk,I [eq. (6.10)-EN1

(where Gkjsup are unfavourable permanent loads and Gkjinf are favourable permanent loads)

or the less favourable of the two following expressions:

) + 1,5 • Vo1Qk,1 + £1,5 • Vo,iQk,i j>1 i>1

E(1,15 • Gkj,sup +1,0 • Gkj,inf) +1,5 • Qk,1 +£1,5 • Vo,iQk,i

The National Annex decides whether eq. [(6.10)-EN1990] or the less favourable of [(6.10a)-EN1990] and [(6.10b)-EN1990] should be considered.

In these expressions G^sup (Gkj,inf) is a set of permanent actions from one source with an unfavourable (or favourable) resulting effect of the total action. For example, all actions originating from the self weight of the structure may be considered as coming from one source; this also applies if different materials are involved. Therefore in the verifications of resistance of the sections of a beam, its self weight should be taken with the same design value for the whole length of the beam ( g = 1,35), whereas a different value of partial factor (yg = 1,0) can be taken for permanent loads originating from a different source.

Combinations of actions with Set C of partial factors (STR/GEO)

£(1,0 • G^ +1,0 • Gkj,inf) +1,3 • Qw + £ 1,3 • ¥o,iQk,i

2.4.4 Verification of static J 1 >'

equilibrium - EQU

2.5 Design assisted by testing

2.6 Supplementary requirements for foundations

2.7 Requirements for fastenings

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